Continuity of this sort of map has been studied in the context of the Baum–Connes assembly conjecture, and was used explicitly by Higson [1]}, Higson–Lafforgue–Skandalis [2]} and later Willett–Yu [3]} to construct counterexamples to the coarse Baum–Connes conjecture. It also appears in the work of Gong–Wang–Yu [4]}, Oyono-Oyono–Yu [5]} and Guentner–Tessera–Yu [6]} in this context, and for the most part all of these results have the common theme that they exploit an idea introduced in [7]} called operator norm localisation:
